Explanation:

Given a right triangle, select a vertex where the hypotenuse and one of the legs meet.

The angle #theta# created by this two sides will be used as a reference point

The side that formed the angle #theta# together with the hypotenuse will be referred to as #adjacent# (side adjacent to the angle). The other side will be referred to as #opposite# (side opposite the angle)

The ratio between the #opposite# and the #"hypotenuse"# is called #"sine" (sin#). The inverse of this ratio is called #"cosecant" (csc#)

#sin theta = "opposite" / "hypotenuse" #

#csc theta = "hypotenuse" / "opposite" = 1 / sin theta#

The ratio between the #adjacent# and the #"hypotenuse"# is called "cosine". The inverse of this ratio is called "secant"

#cos theta = "adjacent" / "hypotenuse" #

#sec theta = "hypotenuse" / "adjacent" = 1 / cos theta#

The ratio between the #opposite# and the #adjacent# is called #"tangent"#. The inverse of this ratio is called #"cotangent"#